There are a couple of ways. As with every play, if you're seeing a production of it, the audience has to accept that this really isn't Oedipus, those lights aren't really the son, the costumes usually aren't made of authentic material, etc, etc. The audience needs to suspend the disbelief, otherwise the play won't be very enjoyable.
When simply reading Oedipus Rex, the reader has to believe that Oedipus never mentioned to Jocasta that he had been abandoned and raised by shepherd, that he killed a man on the way to the kingdom, that he feet had been bound together (or that she had never seen the injuries on his heels.) Readers also need to believe that Jocasta never told him that she had a child that was destined to curse the kingdom that she abandoned in the wilderness. Also, if one of them did tell their story to the other, there was some reason the listener didn't chime in with, "Hey, that kinda sound like something that happened in my life!"
The reader also needs to believe that Oedipus wouldn't have recognized the king (either as the king or as his father) or hadn't seen any resemblance of himself in Jocasta. Also, no one else in kingdom ever mentioned the story of the abandoned child or a family resemblance to Oedipus.
I think in order to believe someone would sleep with their mother you have to suspend your disbelief. I think in order for most plays to be interesting and successful you have to be able to be so taken by the story you suspend your disbelief.
In Oedipus Rex, the audience needs to have a willing suspension of disbelief because it's hard for people to believe the stoey behind how Oedipus ends up back in the kingdom of his father-- the pinning of his feet, being abandoned in a field be a guard, picked up by a shephard then given away, then goes to Corinth where upon hearing his fate (that he will kill his father and have sex with his mother) he leaves and ends up in Thebes, where he does indeed fulfill the prophecy. Upon doing so, he blinds himself with the broaches with his mother's dress (after she has hung herself for having sex with her own son) and then goes into exile.